Unitary equivalent classes of one-dimensional quantum walks II

TL;DR

This paper classifies the unitary equivalence classes of various types of one-dimensional quantum walks, including those with defects, phases, and initial states, providing a comprehensive framework for their analysis.

Contribution

It systematically determines the unitary equivalent classes of multiple one-dimensional quantum walk models, extending previous classifications to include initial states and defects.

Findings

Classified unitary equivalent classes for various quantum walk models

Extended classification to include initial states and defects

Provided a comprehensive framework for analyzing quantum walks

Abstract

This study investigated the unitary equivalent classes of one-dimensional quantum walks. We determined the unitary equivalent classes of one-dimensional quantum walks, two-phase quantum walks with one defect, complete two-phase quantum walks, one-dimensional quantum walks with one defect and translation-invariant one-dimensional quantum walks. The unitary equivalent classes of one-dimensional quantum walks with initial states were also considered.